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WorksheetsCollege Algebra Unit 2 Review
Total questions: 163
Worksheet time: 14hrs 29mins
−1 ∕ 3
− 3
1 ∕ 3
−5 ∕ 3
3
I and II only
I only
II only
II and III only
I, II and III
6
-2
4
3
9
f(x) = 3x2 - 9
y = -2x2+16x+4
y = 2(x-3)2+18
f(x)=-x2+2x+8
Select the correct equation for the graph.
f(x)=-(x+2)²+4
f(x)= (x-2)²+4
f(x)=(x+2)²-4
f(x)=-(x-2)²+4
f(1) = 3 and f(4) = -6.
If g(x) = -3x2 - 5x + 2 = 0, on which interval(s) is g(x) > 0?
(-∞, -2) u (0.333,∞)
(0.333, ∞)
[-2.0, 0.333]
(-2,0.333)
A school club will have spend $0.25 for each lollipop for the first 1000 lollipops it orders for a fundraiser. After that, they will no longer have to purchase future lollipops. Which of the following graphs best models the cost incurred by the school club?
A school club will have spend $0.25 for each lollipop for the first 1000 lollipops it orders for a fundraiser. After that, they will no longer have to purchase future lollipops. Which of the following piece-wise functions best models the cost incurred by the school club?
Which of the following tables of values represents graphs of linear functions?
If the graph of this absolute value function is
f(x) = a|bx + c| + d, what is the value of d in the equation?
-4
3
4
1/2
Which of the following would produce the graph of f (x)?
f(x) = ½ |x - 4| + 3
f(x) = ½ |x + 4| + 3
f(x) = ½ |x - 4| - 3
f(x) = 2 |x - 4| + 3
Which of the following is the maximum point on the graph of f(x) = -x2 + 6x + 4 ?
(3,31)
(-3,-23)
(3,13)
(3,22)
The graph of a square root function, h(x), is pictured above. Which of the following would be the graph of h(x)?
-[√(x-3)]+2
[√(x+3)]+2
[√(x-3)]+2
-[√(x+3)]+2
Which of the following statements are true regarding the graph of h(x) above?
I. The domain of h(x) is [-3,∞).
II. The range of h(x) (-∞,2).
III. The graph of h(x) contains the point (-2,1).
I only
II and III only
II only
I and III only
I, II and III
Regarding the graph of f(x) above, which of the following statements is NOT true?
f(-6) < f(-5) < f(2)
f(-6) < f(1) < f(2)
f(-3) < f(0) < f(1)
f(-2) < f(0) < f(-6)
Cannot be determined
Regarding the graph of f(x) above, which of the following statements is true?
I. The range of f(x) is [-4,8)
II. f(x)=-3 only when x=-2
III. The domain of f(x) is [-6, 3]
I and III only
I, II and III
I and II only
I only
II and III only
Regarding the graph of h(x) above, which of the following intervals includes all the value(s) of x for which h(x) > 0?
(-3,-2)u(2,5)
[-3,5)
[-3,5]
(-3,5)
(-4,-2)U(2,5)
Regarding the graph of h(x) above, which of the following intervals indicates all the value(s) of x for which h(x) is increasing?
(-3,-2)U(2,5)
(-4,5)
[-3,5]
(-3,5)
(-4,-2)U(2,5)
What is the domain of the function f(x) shown in the figure?
[1,∞)
(1,2)U(2,5)(5,∞)
[1,2)U(2,5)(5,∞)
(1,5)U(5,∞)
[1,2)U(2,∞)
Given g(x) provided in the graph and the function
f(x) = -3(x + 4)2 - 1, what is true about the two functions?
The vertex is (-4, -1)
They have the same y-intercept
They both open downward
They have the same axis of symmetry
Determine the domain and range of the function
Domain: All real numbers, Range: All real numbers
Domain: x ≥ -4, Range: All real numbers
Domain: All real numbers, Range: y ≥ -4
Domain: -1 ≤ x ≤ 5, Range: y ≥ -4
The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function:
p= -15x2 +600x +60
What is the maximum profit you can make from selling tickets?
$6060
$20
$600
$10,250
Heather dropped a water balloon over the side of her school building from a height of 80 feet. The approximate height of the balloon at any point during its fall can be represented by the following quadratic equation:
h = -16t2 + 80
About how long did it take for the balloon to reach a height of 30 feet?
1.77 seconds
2.24 seconds
2.45 seconds
2.83 seconds
f(x)=(x+7)2
What is the equation of the quadratic function obtained from vertically stretching the parent function by a factor of 2 and then vertically shifting up 3 units?
f(x)= 2(x-3)2
f(x)= 2(x+3)2
f(x)= 2x2+3
f(x)= (x-2)2+3
The blue is f(x)=|x|, red must be
If the blue is f(x)=x2, then the red must be
If the blue is f(x)=x2, the red must be
y = (x - 2)2 + 7
f(x) = 9-3x
g(x) = 5x-7
Find (f+g)(x).
14x-10
-8x+2
2x+2
2x-2
f(x) = x2+9
g(x) = x-9
Find (f-g)(x).
x2+x+9
x2-x+9
x2-x
x2-x+18
f(x)=x2+1
g(x)=2x-5
Find (f-g)(x)
x2-2x+6
-x2+2x+4
-x2-2x-6
x2-2x-4
f(x) = 4x+8
g(x) = x+3,
Find (f*g)(x)
4x2+24
4x2+20x+24
4x2+12x+24
4x2+4x+24
f(x)=x3-3x
g(x)=-4x+1
Find (f*g)(x)
-4x3-5x2-3
-4x3+2x2-3x
-4x4+x3+12x2-3x
-4x4-x3+12x2+3x
f(n)=2n+1
g(n)=3n
Find (f+g)(n)
5n+1
-5n+1
-2n+1
-6n-1
f(x) = 3x2 + 7x and g(x) = 2x2 - x - 1, find (f + g)(x).
g(x)=4x+5
What is (f+g)(2)
j(x)=3x-2
What is (h/j)(-2)
f(x)=2x + 4
g(x)=3x2 - 1
Find f(x) ⋅ g(x)
6x4 + 12x3 - 4x2 - 8x
-6x3 + 12x2 + 2x - 4
6x3 + 12x2 - 2x - 4
5x2 - 18x + 20
f(x)= x2 - 1
g(x)= x - 1
Find (f/g)(10)
9
11
90
110
Which of the following represent the graph?
What is the domain for the following function?
All real numbers except 2.
All real number except -2.
All real numbers except 4.
All real numbers.
Describe the transformation of the function.
shift left 3 units
shift right 3 units
shift up 3 units
shift down 3 units
Describe the transformation of the function.
shift right by 3 units
shift left by 3 units
shift up by 3 units
shift down by 3 units
Describe the transformations of the function.
Shift up by 2 units
Reflected over the x-axis
Shift down by 2 units
Reflected over the y-axis
Shift up by 2 units
Reflected over the y-axis
Shift left by 2 units
Reflected over the x-axis
Y = -3x2 +7x - 2
y = -8x2 + 3x - 7
f(x) = x2- 8x + 15.
Evaluate f(2).
f(2) = 5
f(2) = 12
f(2) = 10
f(2) = 0.5
What is the value of x when f(x) = 16?
x = 4 only
x = 4 and x = 8
x = 16
Not on the graph
What is the value of x when f(x) = 10?
x = 10 only
x = 4 and x = 8
x = 2 and x = 10
No solution
Evaluate f(3).
f(3) = 0
f(3) = -2
f(3) = 3
f(3) = 4
For what value of x does f(x) = -2?
x = 0
x = -5
x = 3
x = -3
If f(x) = 4x + 7, evaluate f(3).
f(3) = 19
f(3) = 14
f(3) = 5
f(3) = 12
the equation
y = 6x?
What is the domain and range of the function?
Domain: x ≤ 7; Range: all real numbers
Domain: all real numbers; Range: y ≤ 7
What is the domain of the function?
all real numbers except y can't be 0
all real numbers except y can't be 1
all real numbers except x can't be 0
all real numbers except x can't be 1
What is the range of the function?
all real numbers except y can't be 0
all real numbers except y can't be 1
all real numbers except x can't be 0
all real numbers except x can't be 1
What is the y intercept?
x = 1
y = 1
(2,0)
(0,2)
What is the equation shown in this graph?
y = 5 - x2
y = x2 + 5
y = 5x
y = 5 - x3
y = x3 + 5
which of the following equations represents the graph?
y = - x2 + 2
y = - x2 - 2
y = x2 + 2
y = x2 - 2
Which of the following graphs represents the equation y = 2/x
Is the relation a function? Why.
Yes, because the x-value 11 has two y-values pair with it.
Yes, because each x-value has only one y-value paired with it.
No, because the x-value 11 has two y-values pair with it.
No, because each x-value has only one y-value paired with it.
Is the relation a function?
Yes, it is a function.
No, it is not a function.
Which of the relations on the graph CANNOT indicate a function?
A and B
C and D
A, C, D
A, B, C, D
Using the vertical line test, does this graph show a function?
Yes
No
Only sometimes
Not enough information
What is the y intercept of the line with the positive slope?
-2
2
4
0
(1,3) (1,5) (2,6) (3,7)
Is this a valid function?
Yes because all the values map to only one value
No because one domain can't go to two range values
Not enough information
No because one range goes to two domain values
If f(x) (the blue graph) is the parent function, what is the equation of g(x) (the transformed red graph)?
g(x)=x3+1
g(x)=x3-1
g(x)=(x-1)3
g(x)=(x+1)3
Vroom Car Shop charges an hourly labor fee plus the cost of the parts to fix a vehicle.
Jenny’s equation to fix her car is y = 65x + 110.
Henry goes to the same shop and his equation is y = 65x + 80.
Which statement best describes the change?
The hourly rate for Henry was increased.
The hourly rate for Henry was decreased.
The cost of the parts for Henry was more expensive.
The cost of the parts for Henry was less expensive.
If f(x) is the red graph and g(x) is the blue graph, what transformation changes f(x) to g(x)?
translation
rotation
reflection
vertical stretch
Which of the following functions reflects the graph f(x)=(x-1)2 over the y-axis?
g(x)= - (x-1)2
g(x)= (x+1)2
g(x)= (-x-1)2
g(x)= (x-1)2-1
Solve:
2x2 + 5x ≥ 12
[-4, 1.5]
(−∞, -4) U (1.5, ∞)
(−∞, -4] U [1.5, ∞)
no solution
Solve: 5x - 10x2 < 0
(0, ½)
[0, ½]
(−∞, 0) U (½, ∞)
(- ½ , 0)
Solve:
3x - x2 > 0
(−∞, 0) U (3, ∞)
(−∞, - 3) U (0, ∞)
(-3, 0)
(0, 3)
When is this function increasing?
−3 < x < 3
0 < x < 5
0 < x < 55
−5 < x < 0
Where is the function increasing?
x < 1
x > 1
y < −4
y > −4
Where is the function increasing?
(4, ∞)
(−4, ∞)
(6, ∞)
4 < x < 6
Where is the function decreasing?
( −∞, −2.55) U (0, 2.55)
(∞, −6.25) U (36, −6.25)
(−∞, ∞)
(−∞, 0)
Where is the function increasing?
x ≥ −1
x ≤ −1
x ≥ 3
x ≤ 3

Which of the following functions reflects the graph f(x)=(x-1)2 over the x-axis?
g(x)= - (x-1)2
g(x)= (x+1)2
g(x)= (-x-1)2
g(x)= (x-1)2-1
